When is \(\mathrm {Int}(E,D)\) a locally free \(D\)-module
type: Item
instance of: scholarly article
title: When is \(\mathrm {Int}(E,D)\) a locally free \(D\)-module
zbMATH Open document ID: 1402.13020
DOI: 10.1007/978-3-319-74195-6_10
author: Ali Tamoussit
author: Lahoucine Izelgue
publication date: 2018-11-30T00:00:00Z
review text: Let \(D\) be an integral domain with quotient field \(K\). For \(E\subset D\) denote by \(\mathrm{Int}(E,D)\) the \(D\)-module of polynomials \(f\in K[X]\) satisfying \(f(E)\subset D\). The authors give some sufficient conditions for \(\mathrm{Int}(E,D)\) to be locally free, showing in particular that this holds if \(D\) is an almost Krull domain and \(E\) is infinite and residually co-finite with \(D\) (Theorem 2). They prove also that if \(D\) is a locally essential domain and \(E\) is infinite and residually co-finite with \(D\), then \(\mathrm{Int}(E,D)\) is a flat \(D\)-module (Theorem 1). For the entire collection see [Zbl 1392.13001].
reviewed by: Władysław Narkiewicz
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 13B25
Mathematics Subject Classification ID: 13C11
Mathematics Subject Classification ID: 13G05
zbMATH DE Number: 6987345
zbMATH Keywords: Integer-valued polynomials
zbMATH Keywords: flat modules
zbMATH Keywords: locally free modules
zbMATH Keywords: Krull domains
MaRDI profile type: Publication
full work available at URL: 978-3-319-74195-6 10
OpenAlex ID: W2792762912
description: scientific article; zbMATH DE number 6987345